Preface | p. xiii |

Author | p. xvii |

Quantum Principles | |

Perspective and Principles | p. 3 |

Prelude to Quantum Mechanics | p. 3 |

Stern-Gerlach Experiment | p. 7 |

Idealized Stern-Gerlach Results | p. 12 |

Classical Model Attempts | p. 15 |

Wave Functions for Two Physical-Outcome Case | p. 21 |

Process Diagrams, Operators, and Completeness | p. 25 |

Further Properties of Operators | p. 28 |

Operator Reformulation | p. 37 |

Operator Rotation | p. 39 |

Bra-Ket Notation/Basis States | p. 46 |

Transition Amplitudes | p. 47 |

Three-Magnet Setup Example-Coherence | p. 50 |

Hermitian Conjugation | p. 53 |

Unitary Operators | p. 56 |

A Very Special Operator | p. 57 |

Matrix Representations | p. 58 |

Matrix Wave Function Recovery | p. 62 |

Expectation Values | p. 64 |

Wrap Up | p. 65 |

Problems | p. 66 |

Particle Motion in One Dimension | p. 77 |

Photoelectric Effect | p. 77 |

Compton Effect | p. 79 |

Uncertainty Relation for Photons | p. 83 |

Stability of Ground States | p. 85 |

Bohr Model | p. 86 |

Fourier Transform and Uncertainty Relations | p. 88 |

Schrödinger Equation | p. 90 |

Schrödinger Equation Example | p. 94 |

Dirac Delta Functions | p. 97 |

Wave Functions and Probability | p. 99 |

Probability Current | p. 102 |

Time Separable Solutions | p. 103 |

Completeness for Particle States | p. 104 |

Particle Operator Properties | p. 107 |

Operator Rules | p. 110 |

Time Evolution and Expectation Values | p. 112 |

Wrap-Up of Chapter 2 | p. 114 |

Problems | p. 115 |

Some One-Dimensional Solutions to the Schrödinger Equation | p. 121 |

Introduction | p. 121 |

The Infinite Square Well: Differential Solution | p. 123 |

The Infinite Square Well: Operator Solution | p. 129 |

The Finite Potential Barrier Step Potential | p. 134 |

The Harmonic Oscillator | p. 140 |

The Attractive Kronig-Penny Model | p. 149 |

Bound State and Scattering Solutions | p. 155 |

Problems | p. 156 |

Hilbert Space and Unitary Transformations | p. 161 |

Introduction and Notation | p. 161 |

Inner and Outer Operator Products | p. 163 |

Operator-Matrix Relationship | p. 165 |

Hermitian Operators and Eigenkets | p. 166 |

Gram-Schmidt Orthogonalization Process | p. 168 |

Compatible Operators | p. 170 |

Uncertainty Relations and Incompatible Operators | p. 172 |

Simultaneously Measureable Operators | p. 175 |

Unitary Transformations and Change of Basis | p. 176 |

Coordinate Displacements and Unitary Transformations | p. 180 |

Schrödinger and Heisenburg Pictures of Time Evolution | p. 181 |

Free Gaussian Wave Packet in the Heisenberg Picture | p. 184 |

Potentials and the Ehrenfest Theorem | p. 185 |

Problems | p. 186 |

Three Static Approximation Methods | p. 191 |

Introduction | p. 191 |

Time-Independent Perturbation Theory | p. 192 |

Examples of Time-Independent Perturbation Theory | p. 195 |

Aspects of Degenerate Perturbation Theory | p. 198 |

WKB Semiclassical Approximation | p. 198 |

Use of the WKB Approximation in Barrier Penetration | p. 202 |

Use of the WKB Approximation in Bound States | p. 204 |

Variational Methods | p. 207 |

Problems | p. 212 |

Generalization to Three Dimensions | p. 217 |

Cartesian Basis States and Wave Functions in Three Dimensions | p. 217 |

Position/Momentum Eigenket Generation | p. 219 |

Example: Three-Dimensional Infinite Square Well | p. 222 |

Spherical Basis States | p. 224 |

Orbital Angular Momentum Operator | p. 225 |

Effect of Angular Momentum on Basis States | p. 226 |

Energy Eigenvalue Equation and Angular Momentum | p. 230 |

Complete Set of Observables for the Radial Schrödinger Equation | p. 232 |

Specification of Angular Momentum Eigenstates | p. 234 |

Angular Momentum Eigenvectors and Spherical Harmonics | p. 240 |

Completeness and Other Properties of Spherical Harmonics | p. 245 |

Radial Eigenfunctions | p. 248 |

Problems | p. 248 |

Quantum Particles | |

The Three-Dimensional Radial Equation | p. 255 |

Recap of the Situation | p. 255 |

The Free Particle | p. 257 |

The Infinite Spherical Well Potential | p. 264 |

The "Deuteron" | p. 267 |

The Coulomb Potential: Initial Considerations | p. 280 |

The Coulomb Potential: 2-D Harmonic Oscillator Comparison | p. 283 |

The Confined Coulombic Model | p. 299 |

Problems | p. 307 |

Addition of Angular Momenta | p. 317 |

General Angular-Momentum Eigenstate Properties | p. 317 |

Combining Angular Momenta for Two Systems | p. 319 |

Explicit Example of Adding Two Spin 1/2 Systems | p. 324 |

Explicit Example of Adding Orbital Angular Momentum and Spin 1/2 | p. 326 |

Hydrogen Atom and the Choice of Basis States | p. 331 |

Hydrogen Atom and Perturbative Energy Shifts | p. 334 |

Problems | p. 338 |

Spin and Statistics | p. 343 |

The Connection between Spin and Statistics | p. 343 |

Building Wave Functions with Identical Particles | p. 344 |

Particle Occupation Basis | p. 347 |

More on Fermi-Dirac Statistics | p. 352 |

Interaction Operator and Feynman Diagrams | p. 354 |

Implications of Detailed Balance | p. 357 |

Cubical Enclosures and Particle States | p. 362 |

Maxwell-Boltzman Statistics | p. 364 |

Bose-Einstein Statistics | p. 366 |

Fermi-Dirac Statistics | p. 370 |

The Hartree-Fock Equations | p. 375 |

Problems | p. 379 |

Quantum Particle Scattering | p. 387 |

Introduction | p. 387 |

The One-Dimensional Integral Schrödinger Equation | p. 388 |

Reflection and Transmission Amplitudes | p. 392 |

One-Dimensional Delta-Function Scattering | p. 393 |

Step-Function Potential Scattering | p. 396 |

The Born Series | p. 402 |

The Three-Dimensional Integral Schrödinger Equation | p. 404 |

The Helmholtz Equation and Plane Waves | p. 407 |

Cross Sections and the Scattering Amplitude | p. 411 |

Scattering Phase Shifts | p. 412 |

Finite-Range Potential Scattering | p. 416 |

The Three-Dimensional Born Series | p. 421 |

Identical Particle Scattering | p. 426 |

Proton-Proton Scattering | p. 430 |

Problems | p. 434 |

Connecting to the Standard Model | p. 443 |

Discrete Symmetries | p. 443 |

Parity | p. 444 |

Time Reversal | p. 448 |

Charge Conjugation | p. 453 |

Particle Primer | p. 454 |

Particle Interactions | p. 460 |

Quantum Electrodynamics | p. 461 |

Quantum Chromodynamics | p. 463 |

Weak Interactions | p. 468 |

Supersymmetry | p. 472 |

Superstrings | p. 474 |

Postlude | p. 477 |

Helpful Books on Particle and String Physics | p. 477 |

Problems | p. 478 |

Notation Comments and Comparisons | p. 485 |

Lattice Models | p. 487 |

2-D Harmonic Oscillator Wave Function Normalization | p. 493 |

Allowed Standard Model Interactions | p. 495 |

The Ising Model and More | p. 497 |

Weak Flavor Mixing | p. 509 |

Index | p. 523 |

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